cyecca

Cymbolic Estimation and Control with Computer Algebra

A lightweight Python library for robotics and control systems using Lie groups and symbolic mathematics with CasADi.

Features

• Lie Group Library: Complete implementations of SO(2), SO(3), SE(2), SE(3), SE_2(3), and R^n groups with multiple parameterizations
• Type-Safe Modeling Framework: Declarative API for building dynamical systems with full IDE autocomplete support
• Hybrid DAE Systems: Support for continuous/discrete states, algebraic constraints, event detection, and quadrature integration
• Symbolic Mathematics: CasADi-SymPy interoperability with Taylor series approximations and expression simplification
• Code Generation: Automatic C code generation from symbolic expressions for embedded systems
• Numerical Integration: RK4, RK8 (DOP853), and Euler integrators with adaptive stepping
• Trajectory Planning: Bezier curve tools for path planning with derivatives up to snap
• Visualization: CasADi expression graph rendering for debugging and documentation

Installation

git clone https://github.com/CogniPilot/cyecca.git
cd cyecca
poetry install
poetry run ./tools/test.sh   # optional: run tests

Quick Start

# Lie groups for 3D transformations
import cyecca.lie as lie
import casadi as ca

X = lie.SE3Quat.elem(ca.DM([1, 2, 3, 1, 0, 0, 0]))  # position + quaternion
X_inv = X.inverse()

# Type-safe modeling with full autocomplete
from cyecca.dynamics import ModelSX, state, input_var, param, output_var, symbolic

@symbolic
class States:
    x: ca.SX = state(1, 1.0, "position")  # Start at x=1
    v: ca.SX = state(1, 0.0, "velocity")

@symbolic
class Inputs:
    F: ca.SX = input_var(desc="force")

@symbolic
class Params:
    m: ca.SX = param(1.0, "mass")
    c: ca.SX = param(0.1, "damping")
    k: ca.SX = param(1.0, "spring constant")

@symbolic
class Outputs:
    position: ca.SX = output_var(desc="position output")
    velocity: ca.SX = output_var(desc="velocity output")

model = ModelSX.create(States, Inputs, Params, output_type=Outputs)
x, u, p, y = model.x, model.u, model.p, model.y

# Mass-spring-damper: mx'' + cx' + kx = F
f_x = ca.vertcat(x.v, (u.F - p.c * x.v - p.k * x.x) / p.m)

# Output the full state
f_y = ca.vertcat(x.x, x.v)

model.build(f_x=f_x, f_y=f_y, integrator='rk4')

# Simulate free oscillation from x0=1
result = model.simulate(0.0, 10.0, 0.01)
# Output:
#   Final position: -0.529209
#   Final velocity: 0.323980
#   result['out'][0, :] contains position trajectory
#   result['out'][1, :] contains velocity trajectory

Documentation

📚 Read the documentation on GitHub Pages

The full documentation includes:

• Installation guide and quick start tutorial
• Comprehensive Lie groups guide with examples
• Modeling framework guide (hybrid systems, DAE, composition)
• Complete API reference (auto-generated from docstrings)

Interactive Examples: See cyecca_notebooks for Jupyter notebooks with tutorials and demonstrations.

Build locally:

cd docs && poetry run make html
# Open docs/_build/html/index.html in your browser

Modules

Lie Groups (cyecca.lie)

Complete implementations of SO(2), SO(3), SE(2), SE(3), SE_2(3), and R^n with multiple parameterizations.

Key features: Group operations, Lie algebra, Jacobians, conversions Learn more: Lie Groups Guide

Dynamics Framework (cyecca.dynamics)

Type-safe declarative API for building hybrid dynamical systems with IDE autocomplete.

Key features: Continuous/discrete states, events, DAE, composition, linearization Learn more: Modeling Guide

Pre-Built Models (cyecca.models)

Ready-to-use dynamics models: quadrotor, fixed-wing aircraft, RDD2 controller, Bezier trajectories

Path Planning (cyecca.planning)

Dubins path planner for fixed-wing aircraft with forward-only, fixed turn radius constraints.

Key features: CasADi-based symbolic planning, RSL/LSR/LSL/RSR path types, branch-free implementation Learn more: Planning Module

Other Modules

• integrators - RK4, RK8 (DOP853), Euler with adaptive stepping
• symbolic - SymPy ↔ CasADi conversion, Taylor series
• codegen - C code generation for embedded systems
• graph - Expression graph visualization

ROS 2 Integration

Launch files for quadrotor and fixed-wing simulation with RViz visualization, joystick control, and trajectory tracking.

ros2 launch cyecca rdd2_sim.xml        # Quadrotor simulation
ros2 launch cyecca fixedwing_sim.xml   # Fixed-wing simulation

Supported Lie Groups

Dependencies

Core dependencies (automatically installed):

• casadi: Symbolic framework and optimization
• numpy: Numerical computing
• scipy: Scientific computing
• sympy: Symbolic mathematics
• beartype: Runtime type checking
• pydot: Graph visualization

Development

The library is actively used in CogniPilot projects for:

• Flight control system design
• Trajectory optimization
• State estimation
• Hardware-in-the-loop simulation

License

See LICENSE file for details.

Citation

If you use cyecca in your research, please cite:

@software{cyecca,
  title = {cyecca: Symbolic Estimation and Control with Computer Algebra},
  author = {Goppert, James and Lin, Li-Yu and Kmetko, Alex and others},
  organization = {CogniPilot},
  url = {https://github.com/CogniPilot/cyecca},
  year = {2025}
}